CUET Preparation Today
CUET
-- Mathematics - Section B1
Differential Equations
The solution of the differential equation (xy4+y)dx−xdy=0, is |
4x4y3+3x3=Cy3 3x3y4+4y3=Cx3 3x4y3+4x3=Cy3 none of these |
3x4y3+4x3=Cy3 |
We have, (xy4+y)dx−xdy=0 ⇒dydx=xy4+yx ⇒dydx−yx=y4 ⇒1y4dydx+(−1y3)1x=1 Let −y−3=v. Then, 3y−4dydx=dvdx ∴ 13dvdx+vx=1⇒dvdx+3xv=3 ....(i) This is a linear differential equation with integrating factor x3 Multiplying both sides of (i) by x3 and integrating, we get vx3=3x44+C ⇒−x3y3=3x44+C ⇒−4x3=3x4y3+4y3C ⇒3x4y3+4x3=−4Cy3⇒3x4y3+4x3=λy3 |